I think all of us made this experiment in high school:

Push a bar magnet forward and back into a coil inductor. Then, current
will flow in the inductor. The explanation is that the changing of the
magnetic field caused by moving the magnet induces an electric field,
an EMC, in the inductor, that produces the current. This is described
by the law of induction, Maxwell's third equation (that seldom is
mentioned in high school, though): curl E = -dB/dt. Thus: The _change_
in B _causes_ E.

But, from a mathematical standpoint, this seems a little odd. Isn't it
more natural to view the equation this way: The "discrepancy" of E
causes B to change? Here, curl B is considered as a measure of the
"discrepancy" of B. Zero curl means no discrepancy and no change of B.
I'm imagining that the fields try to "flatten out", getting rid of the
discrepancies, viewing the Maxwell's fourth equation, curl H - j = dD/
dt in the same way.

This view seems natural, because if we know E and B (and hence D and
H) at a time, t=0, say, then we can solve Maxwell's equations with
these initial values, and then calculate E and B for all future and
past times.

But if we try to apply this viewpoint to the simple magnet/conductor
experiment above, it doesn't make sense physically. Because then, we
must say that the change in B is caused by E (more precisely, curl E),
and not the other way round. But there wouldn't be any E if we didn't
move the magnet. And B isn't caused by E but by internal processes in
the magnet. These internal processes are unknown (at least by me), but
to get a better understanding, substitute the bar magnet for another,
thin but long, coil inductor with a constant current flowing through
it, thus giving rise to a magnetic field similar to the bar magnet's
field.

By our view, the only that can cause a change in E (or D) is Maxwell's
fourth equation. But in the outer inductor, there is initially no
current, thus dD/dt = curl H there, and H must be caused by the inner
inductor. But then D would change even if the inner inductor (or
original bar magnet) is at rest, unless curl H = 0, but then D
wouldn't change, and there would be no induced current in the (outer)
inductor...

This seems to go in circles, I can't get it to make sense. Can you?

Regards,

Erland Gadde

On May 16, 10:34 am, Erland Gadde <erl...@bredband.net> wrote:
I think all of us made this experiment in high school:

Push a bar magnet forward and back into a coil inductor. Then, current
will flow in the inductor. The explanation is that the changing of the
magnetic field caused by moving the magnet induces an electric field,
an EMC, in the inductor, that produces the current. This is described
by the law of induction, Maxwell's third equation (that seldom is
mentioned in high school, though): curl E = -dB/dt. Thus: The _change_
in B _causes_ E.

But, from a mathematical standpoint, this seems a little odd. Isn't it
more natural to view the equation this way: The "discrepancy" of E
causes B to change? Here, curl B is considered as a measure of the
"discrepancy" of B. Zero curl means no discrepancy and no change of B.
I'm imagining that the fields try to "flatten out", getting rid of the
discrepancies, viewing the Maxwell's fourth equation, curl H - j = dD/
dt in the same way.

This view seems natural, because if we know E and B (and hence D and
H) at a time, t=0, say, then we can solve Maxwell's equations with
these initial values, and then calculate E and B for all future and
past times.

But if we try to apply this viewpoint to the simple magnet/conductor
experiment above, it doesn't make sense physically. Because then, we
must say that the change in B is caused by E (more precisely, curl E),
and not the other way round. But there wouldn't be any E if we didn't
move the magnet. And B isn't caused by E but by internal processes in
the magnet. These internal processes are unknown (at least by me), but
to get a better understanding, substitute the bar magnet for another,
thin but long, coil inductor with a constant current flowing through
it, thus giving rise to a magnetic field similar to the bar magnet's
field.

By our view, the only that can cause a change in E (or D) is Maxwell's
fourth equation. But in the outer inductor, there is initially no
current, thus dD/dt = curl H there, and H must be caused by the inner
inductor. But then D would change even if the inner inductor (or
original bar magnet) is at rest, unless curl H = 0, but then D
wouldn't change, and there would be no induced current in the (outer)
inductor...

This seems to go in circles, I can't get it to make sense. Can you?

Regards,

Erland Gadde

I don't like either interpretation. There is a third, namely that the
changes are simulataneous to each other and thus simply different
perspectives of the same changing system, the cause of which lies
somewhere else. That somewhere else is in turn the motion of the
charged particles themselves, they being the source of all fields.

Consider a simple analogy: A rancher thins his herd by 1 percent each
day. He notices that amount of feed required to sustain the herd
simulataneously changes with the changing cow population. The common
interpretation of Faraday's law is equivalent in logic to stating that
the selling off of cattle "causes" a decreased need for feed.

Maxwell's equations are not *causality* equations. Maxwell clearly
understood this.
YES! For a simplistic view, look in Wikipedia under "Jefimenko's Equations."
For a detailed discussion of Causality and Induction, please run -- don't
walk -- to your nearest Amazon.com and get his Causality Electromagnetic
Induction and Gravitation. Best $25 you'll ever spend.

This 'problem with induction', which also bothered Einstein at the

the law of induction, Maxwell's third equation
(that seldom is mentioned in high school, though):
curl E = -dB/dt.

curl E causes B to change? -- more natural, mathematically.

LATERAL (ad-hoc) force: vs GRAViTATiONAL force:

F = m a || Fg = m1*g
expresses the fact that || expresses the fact that
a force F causes an object || a weight Fg causes an object
to move with acceleration || to move with acceleration
a = F/m, || g = Fg/m1,
or that an object in order || or that an object in order
to get an acceleration a, || to get an acceleration g,
needs a force || needs a weight (i.e. force)
F = m a || Fg = m1*g
to be applied to it. || to be applied to it.

Mathematically it could || Mathematically, it could
just as well tell you that || just as well tell you that
an object with acceleration || an object with acceleration
a causes a force || g causes a weight (i.e. force)
F = m a. || Fg = m1*g
|| = G*M*m1/(n - 1)*rA^2
$$ || = 4*(pi)^2*m1*lbob/(tbob)^2.

Assume LATERAL F force is equal to GRAViTATiONAL F_g at, rA and M:

CONCLUSiON a: || CONCLUSiON g:
ACCELERATiON a varies with || ACCELERATiON g is *independent*
mass m (FORCE F_a constant). || of *MAGNiTUDE*, of TEST mass m1.

Acceleration isN'T CONSTANT. || Acceleration g CONSTANT @ rA & M.
The acceleration a *ad-hoc*. || Acceleration g is *rationalized*.

On May 18, 4:14 pm, "Bill Miller" <BillMillerKT...@worldnet.att.net
wrote:
Maxwell's equations are not *causality* equations. Maxwell clearly
understood this.
YES! For a simplistic view, look in Wikipedia under "Jefimenko's
Equations."
For a detailed discussion of Causality and Induction, please run -- don't
walk -- to your nearest Amazon.com and get his Causality Electromagnetic
Induction and Gravitation. Best $25 you'll ever spend.

This 'problem with induction', which also bothered Einstein at the
start of his 1905 Relativity paper, illustrates the problem of
learning physics from textbook authors who only follow the earlier
generation of textbook authors & don't bother to read the original
material from the "Masters".
Maxwell knew that induction was the direct result of his central
physical concept: electro-kinetic momentum (or as it is now known,
'vector potential'). In his groundbreaking 1864 essay "A Dynamical
Theory of the Electromagnetic Field" (republished in 1996, edited by
Thomas F. Torrance) he gave pride of place to this concept in his his
list of equations of the EM field (page 6. This was also the focus
for Maxwell's contemporary, L. V. Lorenz with his study of what we now
refer to as the 4-potential in 1867. It was Oliver Heaviside who
eliminated all reference to this concept (see Bruce J. Hunt's "The
Maxwellians" 1991) when he rewrote Maxwell's equations into what is
now known as Maxwell's (Duplex Vector) Equations involving only EM
field variables. This was acceptable in the 19th Century as the EM
field was viewed as EXISTING in the luminiferous aether. It is no
longer acceptable when we know that electricity is particulate
(electrons) & we no longer believe in the aether. None-the-less, EM
theory is still taught from this erroneous field viewpoint when the
electro-kinetic model is still valid for point-charges. I have tried
to get people interested in the series of papers written by C. J.
Carpenter, Professor of Electrical Engineering, who has clearly
demonstrated the value of this alternative viewpoint over the field
approach when solving real-world electrical problems. Feynman also
realized the importance of the vector potential, as did his 'star'
pupil (Carver Meade) when he wrote "Collective Electrodynamics".
The lack of response to my challenge to the EM field theorists in
solving the 100 year old problem of two-electron scattering shows that
the field approach is just an elegant but empty mathematical approach
to the fundamentals of EM. If you feel you really understand classical
EM you may wish to respond at:
http://groups.google.com/group/sci.physics.foundations/browse_frm/thread/45c6ef794120973/42a85b126255e277?hl=en#42a85b126255e277
I would like to join Bill in encouraging readers to buy Jefimenko's
masterpiece (see above) as the most logical way of developing the
field theory model of EM.

Hello Herb...

Erland Gadde wrote:
I think all of us made this experiment in high school:

Push a bar magnet forward and back into a coil inductor. Then, current
will flow in the inductor. The explanation is that the changing of the
magnetic field caused by moving the magnet induces an electric field,
an EMC, in the inductor, that produces the current. This is described
by the law of induction, Maxwell's third equation (that seldom is
mentioned in high school, though): curl E = -dB/dt. Thus: The _change_
in B _causes_ E.

Actually Maxwell's equations do NOT solve or "explain" the above
experiment!
First off, B is not changing. There is no dB/dt as the B is fixed to
the magnet and constant.

The "true" situation is that you are moving a magnetic field past a
wire coil creating relative motion in exactly the same way as a moving
wire in a magnetic field (generator) creates an emf. The operative
equation is qV x B. That equation is NOT part of Maxwell's set.

Now here is where things get interesting. How does one "explain"
induction when things are NOT moving? The classic experiment is two
coils of wire. One to a galvanometer and one to a battery. When you
close the circuit to the battery, the meter jumps. But NOTHING is now
moving relative to each other?

It is known that the first coil creates a magnetic field at the second
coil when the current flows, but that is NOT the answer to the
mystery. One can easily show (toroid or outside a long solenoid) that
induction occurs not only where there is no motion, but ALSO happens
when there is NO magnetic field present at the wire in which the
voltage is induced!!!

So what in hell is going on? The secret is that induction is the
result NOT of a changing B field but rather a changing Vector Magnetic
Potential field! As Feynman has suggested, A may actually be MORE
fundamental than B! B is of course obtainable as the curl of A, but
induction requires a non-zero A and yet occurs in regions of zero B.

Adding to the confusion is the fact that if one calculates the
magnetic flux (B integerated over the area of the wire loop) OFTEN
(but not always!) one finds that such an operation gives the induced
potential even if the B field inside the loop does not extend to the
loop itself. This is very odd in that one has to ask just HOW the wire
loop "knows" that flux is pouring through it's center? Clearly an
"explanation" requires some kind of bogus "action at a distance"
theory. Nay. Things stay much more clear if you stick with A and
forget about the Flux thing which just happens to work sometimes.

On May 16, 10:34 am, Erland Gadde <erl...@bredband.net> wrote:





I think all of us made this experiment in high school:

Push a bar magnet forward and back into a coil inductor. Then, current
will flow in the inductor. The explanation is that the changing of the
magnetic field caused by moving the magnet induces an electric field,
an EMC, in the inductor, that produces the current. This is described
by the law of induction, Maxwell's third equation (that seldom is
mentioned in high school, though): curl E = -dB/dt. Thus: The _change_
in B _causes_ E.

But, from a mathematical standpoint, this seems a little odd. Isn't it
more natural to view the equation this way: The "discrepancy" of E
causes B to change? Here, curl B is considered as a measure of the
"discrepancy" of B. Zero curl means no discrepancy and no change of B.
I'm imagining that the fields try to "flatten out", getting rid of the
discrepancies, viewing the Maxwell's fourth equation, curl H - j = dD/
dt in the same way.

This view seems natural, because if we know E and B (and hence D and
H) at a time, t=0, say, then we can solve Maxwell's equations with
these initial values, and then calculate E and B for all future and
past times.

But if we try to apply this viewpoint to the simple magnet/conductor
experiment above, it doesn't make sense physically. Because then, we
must say that the change in B is caused by E (more precisely, curl E),
and not the other way round. But there wouldn't be any E if we didn't
move the magnet. And B isn't caused by E but by internal processes in
the magnet. These internal processes are unknown (at least by me), but
to get a better understanding, substitute the bar magnet for another,
thin but long, coil inductor with a constant current flowing through
it, thus giving rise to a magnetic field similar to the bar magnet's
field.

By our view, the only that can cause a change in E (or D) is Maxwell's
fourth equation. But in the outer inductor, there is initially no
current, thus dD/dt = curl H there, and H must be caused by the inner
inductor. But then D would change even if the inner inductor (or
original bar magnet) is at rest, unless curl H = 0, but then D
wouldn't change, and there would be no induced current in the (outer)
inductor...

This seems to go in circles, I can't get it to make sense. Can you?

Regards,

Erland Gadde

I don't like either interpretation. There is a third, namely that the
changes are simulataneous to each other and thus simply different
perspectives of the same changing system, the cause of which lies
somewhere else. That somewhere else is in turn the motion of the
charged particles themselves, they being the source of all fields.

Consider a simple analogy: A rancher thins his herd by 1 percent each
day. He notices that amount of feed required to sustain the herd
simulataneously changes with the changing cow population. The common
interpretation of Faraday's law is equivalent in logic to stating that
the selling off of cattle "causes" a decreased need for feed

Hello Herb...

See! I took your (excellent) advice! Thanks for steering me in this
direction.

Carpenter's papers are a bit difficult to access. They are located within
the IEEE site and unless one is an IEEE member -- or have a friend -- you
are kinda screwed.

BUT... Kirk McDonald has transferred many important EM papers into his site
where they may be viewed. Among them are most of Carpenter's papers. Try
this link:

http://puhep1.princeton.edu/~mcdonald/examples/EM/

Thank you, Bill for your very kind remarks but thank you a thousand

On May 16, 12:34 pm, Erland Gadde <erl...@bredband.net> wrote:
I think all of us made this experiment in high school:

Push a bar magnet forward and back into a coil inductor. Then, current
will flow in the inductor. The explanation is that the changing of the
magnetic field caused by moving the magnet induces an electric field,
an EMC, in the inductor, that produces the current. This is described
by the law of induction, Maxwell's third equation (that seldom is
mentioned in high school, though): curl E = -dB/dt. Thus: The _change_
in B _causes_ E.

But, from a mathematical standpoint, this seems a little odd. Isn't it
more natural to view the equation this way: The "discrepancy" of E
causes B to change? Here, curl B is considered as a measure of the
"discrepancy" of B. Zero curl means no discrepancy and no change of B.
I'm imagining that the fields try to "flatten out", getting rid of the
discrepancies, viewing the Maxwell's fourth equation, curl H - j = dD/
dt in the same way.

This view seems natural, because if we know E and B (and hence D and
H) at a time, t=0, say, then we can solve Maxwell's equations with
these initial values, and then calculate E and B for all future and
past times.

But if we try to apply this viewpoint to the simple magnet/conductor
experiment above, it doesn't make sense physically. Because then, we
must say that the change in B is caused by E (more precisely, curl E),
and not the other way round. But there wouldn't be any E if we didn't
move the magnet. And B isn't caused by E but by internal processes in
the magnet. These internal processes are unknown (at least by me), but
to get a better understanding, substitute the bar magnet for another,
thin but long, coil inductor with a constant current flowing through
it, thus giving rise to a magnetic field similar to the bar magnet's
field.

By our view, the only that can cause a change in E (or D) is Maxwell's
fourth equation. But in the outer inductor, there is initially no
current, thus dD/dt = curl H there, and H must be caused by the inner
inductor. But then D would change even if the inner inductor (or
original bar magnet) is at rest, unless curl H = 0, but then D
wouldn't change, and there would be no induced current in the (outer)
inductor...

This seems to go in circles, I can't get it to make sense. Can you?

It does go in circles. To unify the Coulomb force with the
the magnetic force, use the integral form, then time isn't
conscripted into the mechanism.

http://en.wikipedia.org/wiki/Multiple_integral#Some_practical_applications
http://en.wikipedia.org/wiki/Multiple_integral

Time-independent Maxwell equations
Time-dependent Maxwell's equations
http://farside.ph.utexas.edu/teaching/em/lectures/lectures.html

Maxwell's equations in classic electrodynamics
(classic field theory)_
a) Maxwell equations (no movement),
b) Maxwell equations (with moved bodies)

http://www.wolfram-stanek.de/maxwell_equations.htm#maxwell_classic_extended

Sue...


Regards,

Erland Gadde

That's not even remotely true. The B field for a permanent magnetic
is neither fixed nor constant. A permanent magnet is a magnetic
dipole and possesses the same type of field that changes in both
magnitude and direction about the magnet. So the flux through the
coil is constantly changing as the magnetic moves through it.
Faraday's law, which is one of Maxwell's equations, covers this quite
well.

The "true" situation is that you are moving a magnetic field past a
wire coil creating relative motion in exactly the same way as a moving
wire in a magnetic field (generator) creates an emf. The operative
equation is qV x B. That equation is NOT part of Maxwell's set.

That's the magnetic force. I suppose you could use it to explain
induction, but I think the integral form of Faraday's law is much more
elegant, since it relates a change in magnetic flux to induced emf
directly.

Now here is where things get interesting. How does one "explain"
induction when things are NOT moving? The classic experiment is two
coils of wire. One to a galvanometer and one to a battery. When you
close the circuit to the battery, the meter jumps. But NOTHING is now
moving relative to each other?

There doesn't have to be anything moving. The magnetic fields are now
explicitely changing in time as the current comes up to speed. Once
the current reaches its steady value, this effect stops.

It is known that the first coil creates a magnetic field at the second
coil when the current flows, but that is NOT the answer to the
mystery. One can easily show (toroid or outside a long solenoid) that
induction occurs not only where there is no motion, but ALSO happens
when there is NO magnetic field present at the wire in which the
voltage is induced!!!

I'm not sure what you mean by that. Any conductor under a potential
difference will have a current flowing, and a magnetic field
associated with it by Ampere's law. Unless you're confusing this with
the Aharonov-Bohm effect, which is an entirely different thing.

So what in hell is going on? The secret is that induction is the
result NOT of a changing B field but rather a changing Vector Magnetic
Potential field! As Feynman has suggested, A may actually be MORE
fundamental than B! B is of course obtainable as the curl of A, but
induction requires a non-zero A and yet occurs in regions of zero B.

Quantum mechanically, that seems to be the case. Yet, I've never
heard of this sort of effect applied to the concept of classical
induction. Please enlighten me if you have more info.

mathematical function of it's value throughout space.
its, shithead

You on the other hand are calling "the field" simply as it's value at
its, shithead
a given point in space. Hence you say, it's not fixed but changes
magnitude and direction as you move around. This is really just a
language thing so lets not beat a dead horse and go on. We both really
let's
know what is going on.

The only problem is it just ain't so! I can wind a toroid where one
can measure NO magnetic field outside the coil and yet a loop placed
there will receive the energy transmitted by the toroid! It does that

in a region of ZERO B! In Feynman's lectures he notes how a quantum-
mechanical diffraction shift is induced outside of long solenoids
where again the B field is zero. (which is of course the classic
Aharonov-Bohm effect) Clearly it is something OTHER than the B field
that is jumping through the luminiferous aether! And given that

induction:
Ampere tried to tell us the following:
A bar magnet supports an electrical field whose geometry is a direction of
electrical field which is tangential to the bar, and the only difference of
the field is its clockwise or counterclockwise direction of the electrical
field which determines whether it posessess a north or south magnetic pole
field. This particular attribute of the field is one of many, which include
direction of propigation, strength of field, variation of charge density
along the path of propigation. etc.
Any target material which have magnetic attributes also have their own
electrical field.
When two or more of these fields meet they add or subtract using
conventional algorythmatic math.
Remembet the fields must be curved to respond in a magnetic fashion.
The target materials must accomidate the new electrical squeeze play by a
process which I call a re-direction of inertia. causing the visual
appearance of a magnetic attraction as if a force existed between host and
target,
but alas the force is purely an illusion and is only local to the host and
target. The force (magnetic does not bridge the gap but the dynamic
electrical field proposed by Ampere does). The charged particals simply are
seeking a fresh path of lest resistance and in so doing manifest the
observible magnetic field of which mountains of empirical data have been
yielded.

If you wish to observe a reaction of a dynamic electrical field Tangential
to a bar magnet just position one near a crt screen and observe how
electrons in motion respond to the amperian tangential electrical field.

BTW Gravitation is also a re-direction of inertia but the Amperian dynamic
electrical fields are not curved.
Kind regards, Lee Pugh "Dissident"

"Sue..." <suzysewns...@yahoo.com.au> wrote in message

news:1179515643.637093.186810@l77g2000hsb.googlegroups.com...



On May 16, 12:34 pm, Erland Gadde <erl...@bredband.net> wrote:
I think all of us made this experiment in high school:

Push a bar magnet forward and back into a coil inductor. Then, current
will flow in the inductor. The explanation is that the changing of the
magnetic field caused by moving the magnet induces an electric field,
an EMC, in the inductor, that produces the current. This is described
by the law of induction, Maxwell's third equation (that seldom is
mentioned in high school, though): curl E = -dB/dt. Thus: The _change_
in B _causes_ E.

But, from a mathematical standpoint, this seems a little odd. Isn't it
more natural to view the equation this way: The "discrepancy" of E
causes B to change? Here, curl B is considered as a measure of the
"discrepancy" of B. Zero curl means no discrepancy and no change of B.
I'm imagining that the fields try to "flatten out", getting rid of the
discrepancies, viewing the Maxwell's fourth equation, curl H - j = dD/
dt in the same way.

This view seems natural, because if we know E and B (and hence D and
H) at a time, t=0, say, then we can solve Maxwell's equations with
these initial values, and then calculate E and B for all future and
past times.

But if we try to apply this viewpoint to the simple magnet/conductor
experiment above, it doesn't make sense physically. Because then, we
must say that the change in B is caused by E (more precisely, curl E),
and not the other way round. But there wouldn't be any E if we didn't
move the magnet. And B isn't caused by E but by internal processes in
the magnet. These internal processes are unknown (at least by me), but
to get a better understanding, substitute the bar magnet for another,
thin but long, coil inductor with a constant current flowing through
it, thus giving rise to a magnetic field similar to the bar magnet's
field.

By our view, the only that can cause a change in E (or D) is Maxwell's
fourth equation. But in the outer inductor, there is initially no
current, thus dD/dt = curl H there, and H must be caused by the inner
inductor. But then D would change even if the inner inductor (or
original bar magnet) is at rest, unless curl H = 0, but then D
wouldn't change, and there would be no induced current in the (outer)
inductor...

This seems to go in circles, I can't get it to make sense. Can you?

It does go in circles. To unify the Coulomb force with the
the magnetic force, use the integral form, then time isn't
conscripted into the mechanism.

http://en.wikipedia.org/wiki/Multiple_integral#Some_practical_applica...
http://en.wikipedia.org/wiki/Multiple_integral

Time-independent Maxwell equations
Time-dependent Maxwell's equations
http://farside.ph.utexas.edu/teaching/em/lectures/lectures.html

Maxwell's equations in classic electrodynamics
(classic field theory)_
a) Maxwell equations (no movement),
b) Maxwell equations (with moved bodies)

http://www.wolfram-stanek.de/maxwell_equations.htm#maxwell_classic_ex...





Sue...

Regards,

Erland Gadde- Hide quoted text -

- Show quoted text -- Hide quoted text -

- Show quoted text -

...
So what in hell is going on? The secret is that induction is the
result NOT of a changing B field but rather a changing Vector Magnetic
Potential field! As Feynman has suggested, A may actually be MORE
fundamental than B! B is of course obtainable as the curl of A, but
induction requires a non-zero A and yet occurs in regions of zero B.

Adding to the confusion is the fact that if one calculates the
magnetic flux (B integerated over the area of the wire loop) OFTEN
(but not always!) one finds that such an operation gives the induced
potential even if the B field inside the loop does not extend to the
loop itself. This is very odd in that one has to ask just HOW the wire
loop "knows" that flux is pouring through it's center? Clearly an
"explanation" requires some kind of bogus "action at a distance"
theory. Nay. Things stay much more clear if you stick with A and
forget about the Flux thing which just happens to work sometimes.

Right on, Benj. Please re-read my May 18 post above & follow up with

Right on, Benj. Please re-read my May 18 post above & follow up with
Carpenter's papers from McDonald's website referenced in Bill Miller's
May 19 post. Local vector potential (A) due to remote, retarded
variations in current (J) explain ALL of classical EM.

On Jun 2, 12:34 am, Benj <bjac...@iwaynet.net> wrote:> mathematical ...

its, shithead

...
its, shithead
...
If you cannot communicate in a civilized manner, please refrain from